The following query will list active FND users and their active responsibility assignments:
SELECT fu.user_name , fr.responsibility_name FROM fnd_user fu , fnd_user_resp_groups_direct furgd , fnd_responsibility_vl fr WHERE TRUNC(SYSDATE) BETWEEN TRUNC(fu.start_date) AND NVL(TRUNC(fu.end_date),SYSDATE + 1) AND fu.user_id = furgd.user_id AND TRUNC(SYSDATE) BETWEEN TRUNC(furgd.start_date) AND NVL(TRUNC(furgd.end_date),SYSDATE + 1) AND fr.responsibility_id = furgd.responsibility_id AND TRUNC(SYSDATE) BETWEEN TRUNC(fr.start_date) AND NVL(TRUNC(fr.end_date),SYSDATE + 1) ORDER BY 1,2 ;